CDF‐quantile distributions for modelling random variables on the unit interval

Smithson, Michael; Shou, Yiyun

doi:10.1111/bmsp.12091

Cited by 45 publications

(70 citation statements)

References 55 publications

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“…As detailed in Smithson and Shou (2017), the maximum likelihood estimators are well-behaved for the CDF-quantile family. Their sampling distributions closely approximate the normal distribution for modest sample sizes, and they are relatively stable in the presence of outliers.…”

Section: Cdf-quantile Regressionmentioning

confidence: 98%

“…All of the CDF-quantile distributions in the cdfquantreg package have this form. Explications and examples of members with other combinations of D 1 and D 2 are provided in Smithson and Shou (2017). The distributions in Equation 3 are related to the T-X family in Equation 2 by setting F = R and U [H −1 (S(x), µ, σ)] = W (S(x)), with H differentiable and x ∈ (0, 1).…”

Section: The Distribution Familymentioning

confidence: 99%

“…We name these distributions with the nomenclature F-H (e.g., Cauchit-logistic and logit-Cauchy). Other relevant properties shared by the members of the family included in this package are as follows (proofs are provided in Smithson and Shou 2017): and the Cauchy CDF…”

Section: The Distribution Familymentioning

confidence: 99%

“…The help display also describes the shape of each distribution. We briefly review them here; for more details see Smithson and Shou (2017). We have found that these distributions exhibit four kinds of characteristic shapes, which can be described by their density's tail behavior at the boundaries of the (0, 1) interval:…”

Section: General Usagementioning

confidence: 99%

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mentioning

confidence: 99%

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cdfquantreg: An R Package for CDF-Quantile Regression

Shou¹,

Smithson²

2019

J. Stat. Soft.

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The CDF-quantile family of two-parameter distributions with support (0, 1) described in Smithson and Merkle (2014) and recently elaborated by Smithson and Shou (2017), considerably expands the variety of distributions available for modeling random variables on the unit interval. This family is especially useful for modeling quantiles, and also sometimes out-performs the other distributions. The distributions are very tractable, with a location and dispersion parameter, explicit probability distribution functions, cumulative distribution functions, and quantiles. They enable a wide variety of quantile regression models with predictors for the location and dispersion parameters, and simple interpretations of those parameters. The R package cdfquantreg (Shou and Smithson 2019) (at least R 3.2.0) presented in this paper includes 36 distributions from the CDF-quantile family. Separate submodels may be specified for the location and for the dispersion parameters, with different or overlapping sets of predictors in each. The package offers maximum likelihood, Bayesian MCMC, and bootstrap estimation methods. Model diagnostics, including the gradient, three types of residuals, and the dfbeta influence measures, are available for evaluating models. The package also provides pseudo-random generators for all of its distributions. Many of its functions and their usage have forms familiar to R users, and the documentation is extensive. We also present a SAS macro for general linear models using the CDF-quantile family that includes many of the same capabilities as the cdfquantreg package. The paper provides examples of applications to real data-sets.

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Section: Cdf-quantile Regressionmentioning

confidence: 98%

Section: The Distribution Familymentioning

confidence: 99%

Section: The Distribution Familymentioning

confidence: 99%

Section: General Usagementioning

confidence: 99%

“…

…”

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confidence: 99%

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cdfquantreg: An R Package for CDF-Quantile Regression

Shou¹,

Smithson²

2019

J. Stat. Soft.

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A broad class of zero‐or‐one inflated regression models for rates and proportions

Queiroz

Lemonte

2020

Can J Statistics

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We introduce a family of distributions with bounded support for continuous rates or proportions when the data contain zeros or ones. On the basis of this class of distributions, we propose a novel class of regression models which is useful for modelling fractional data observed on [0, 1) or (0, 1]. The response variable of the new class of regression models has a mixed continuous-discrete distribution with probability mass at zero or one, and the parameters of the mixture distribution are modelled through regression structures involving covariates and unknown parameters. An advantage of this class of regression models is the ability to deal with atypical observations. We consider a frequentist approach to performing inferences, and the traditional maximum likelihood method is employed to estimate the regression parameters. We also propose a residual analysis for the novel class of regression models to assess departures from model assumptions. Additionally, global and local influence methods are discussed. An empirical application that employs real data is considered to illustrate the usefulness of the new class of regression models in practice.

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On a heavy-tailed parametric quantile regression model for limited range response variables

Lemonte

Moreno-Arenas

2019

Comput Stat

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CDF‐quantile distributions for modelling random variables on the unit interval

Cited by 45 publications

References 55 publications

cdfquantreg: An R Package for CDF-Quantile Regression

cdfquantreg: An R Package for CDF-Quantile Regression

A broad class of zero‐or‐one inflated regression models for rates and proportions

On a heavy-tailed parametric quantile regression model for limited range response variables

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